TSTP Solution File: RNG081+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:54:54 EDT 2023

% Result   : Theorem 10.00s 3.32s
% Output   : CNFRefutation 10.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   69 (  19 unt;  33 typ;   0 def)
%            Number of atoms       :  110 (  59 equ)
%            Maximal formula atoms :   40 (   3 avg)
%            Number of connectives :  101 (  27   ~;  21   |;  45   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   53 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  15   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-2 aty)
%            Number of variables   :   28 (;  14   !;  14   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aVector0 > aScalar0 > aNaturalNumber0 > sdtpldt0 > sdtlbdtrb0 > sdtasdt0 > sdtasasdt0 > #nlpp > szszuzczcdt0 > sziznziztdt0 > smndt0 > aDimensionOf0 > xt > xs > sz0z00 > sz00 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xt,type,
    xt: $i ).

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

tff(sdtlbdtrb0,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_15',type,
    '#skF_15': $i ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff(sziznziztdt0,type,
    sziznziztdt0: $i > $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(sz00,type,
    sz00: $i ).

tff('#skF_7',type,
    '#skF_7': $i ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff('#skF_16',type,
    '#skF_16': $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(aDimensionOf0,type,
    aDimensionOf0: $i > $i ).

tff('#skF_14',type,
    '#skF_14': $i ).

tff('#skF_5',type,
    '#skF_5': $i ).

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff(sz0z00,type,
    sz0z00: $i ).

tff(smndt0,type,
    smndt0: $i > $i ).

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff(aScalar0,type,
    aScalar0: $i > $o ).

tff(xs,type,
    xs: $i ).

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(sdtasasdt0,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff(aVector0,type,
    aVector0: $i > $o ).

tff(f_70,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

tff(f_104,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => ( ( sdtpldt0(W0,sz0z00) = W0 )
        & ( sdtpldt0(sz0z00,W0) = W0 )
        & ( sdtasdt0(W0,sz0z00) = sz0z00 )
        & ( sdtasdt0(sz0z00,W0) = sz0z00 )
        & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 )
        & ( sdtpldt0(smndt0(W0),W0) = sz0z00 )
        & ( smndt0(smndt0(W0)) = W0 )
        & ( smndt0(sz0z00) = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

tff(f_239,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

tff(f_436,negated_conjecture,
    ~ ( ( ( aDimensionOf0(xs) != sz00 )
       => ? [W0] :
            ( aVector0(W0)
            & ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
            & ! [W1] :
                ( aNaturalNumber0(W1)
               => ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
            & ( W0 = sziznziztdt0(xs) )
            & ? [W1] :
                ( aVector0(W1)
                & ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
                & ! [W2] :
                    ( aNaturalNumber0(W2)
                   => ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
                & ( W1 = sziznziztdt0(xt) )
                & ? [W2] :
                    ( aScalar0(W2)
                    & ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
                    & ? [W3] :
                        ( aScalar0(W3)
                        & ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
                        & ? [W4] :
                            ( aScalar0(W4)
                            & ( W4 = sdtasasdt0(W0,W0) )
                            & ? [W5] :
                                ( aScalar0(W5)
                                & ( W5 = sdtasasdt0(W1,W1) )
                                & ? [W6] :
                                    ( aScalar0(W6)
                                    & ( W6 = sdtasasdt0(W0,W1) )
                                    & ? [W7] :
                                        ( aScalar0(W7)
                                        & ( W7 = sdtasdt0(W2,W2) )
                                        & ? [W8] :
                                            ( aScalar0(W8)
                                            & ( W8 = sdtasdt0(W3,W3) )
                                            & ? [W9] :
                                                ( aScalar0(W9)
                                                & ( W9 = sdtasdt0(W2,W3) )
                                                & ? [W10] :
                                                    ( aScalar0(W10)
                                                    & ( W10 = sdtasdt0(W4,W8) )
                                                    & ? [W11] :
                                                        ( aScalar0(W11)
                                                        & ( W11 = sdtasdt0(W6,W9) )
                                                        & ? [W12] :
                                                            ( aScalar0(W12)
                                                            & ( W12 = sdtasdt0(W7,W5) )
                                                            & ? [W13] :
                                                                ( aScalar0(W13)
                                                                & ( W13 = sdtasdt0(W10,W12) )
                                                                & sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
                                                                & sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
                                                                & sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
                                                                & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
     => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_328,hypothesis,
    ( aVector0(xs)
    & aVector0(xt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).

tff(f_310,axiom,
    ! [W0,W1] :
      ( ( aVector0(W0)
        & aVector0(W1) )
     => ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = sz00 ) )
       => ( sdtasasdt0(W0,W1) = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).

tff(f_339,hypothesis,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).

tff(c_22,plain,
    aScalar0(sz0z00),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_316,plain,
    ! [W0_16462] :
      ( ( sdtasdt0(sz0z00,W0_16462) = sz0z00 )
      | ~ aScalar0(W0_16462) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_324,plain,
    sdtasdt0(sz0z00,sz0z00) = sz0z00,
    inference(resolution,[status(thm)],[c_22,c_316]) ).

tff(c_405,plain,
    ! [W0_16471] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(W0_16471,W0_16471))
      | ~ aScalar0(W0_16471) ),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_408,plain,
    ( sdtlseqdt0(sz0z00,sz0z00)
    | ~ aScalar0(sz0z00) ),
    inference(superposition,[status(thm),theory(equality)],[c_324,c_405]) ).

tff(c_410,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_408]) ).

tff(c_122,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(cnfTransformation,[status(thm)],[f_436]) ).

tff(c_124,plain,
    ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | ( aDimensionOf0(xs) = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_436]) ).

tff(c_195,plain,
    aDimensionOf0(xs) = sz00,
    inference(negUnitSimplification,[status(thm)],[c_122,c_124]) ).

tff(c_116,plain,
    aVector0(xs),
    inference(cnfTransformation,[status(thm)],[f_328]) ).

tff(c_9723,plain,
    ! [W0_16654,W1_16655] :
      ( ( sdtasasdt0(W0_16654,W1_16655) = sz0z00 )
      | ( aDimensionOf0(W1_16655) != sz00 )
      | ( aDimensionOf0(W1_16655) != aDimensionOf0(W0_16654) )
      | ~ aVector0(W1_16655)
      | ~ aVector0(W0_16654) ),
    inference(cnfTransformation,[status(thm)],[f_310]) ).

tff(c_9729,plain,
    ! [W0_16654] :
      ( ( sdtasasdt0(W0_16654,xs) = sz0z00 )
      | ( aDimensionOf0(xs) != sz00 )
      | ( aDimensionOf0(xs) != aDimensionOf0(W0_16654) )
      | ~ aVector0(W0_16654) ),
    inference(resolution,[status(thm)],[c_116,c_9723]) ).

tff(c_10271,plain,
    ! [W0_16660] :
      ( ( sdtasasdt0(W0_16660,xs) = sz0z00 )
      | ( aDimensionOf0(W0_16660) != sz00 )
      | ~ aVector0(W0_16660) ),
    inference(demodulation,[status(thm),theory(equality)],[c_195,c_195,c_9729]) ).

tff(c_10280,plain,
    ( ( sdtasasdt0(xs,xs) = sz0z00 )
    | ( aDimensionOf0(xs) != sz00 ) ),
    inference(resolution,[status(thm)],[c_116,c_10271]) ).

tff(c_10287,plain,
    sdtasasdt0(xs,xs) = sz0z00,
    inference(demodulation,[status(thm),theory(equality)],[c_195,c_10280]) ).

tff(c_120,plain,
    aDimensionOf0(xt) = aDimensionOf0(xs),
    inference(cnfTransformation,[status(thm)],[f_339]) ).

tff(c_231,plain,
    aDimensionOf0(xt) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_195,c_120]) ).

tff(c_114,plain,
    aVector0(xt),
    inference(cnfTransformation,[status(thm)],[f_328]) ).

tff(c_9727,plain,
    ! [W0_16654] :
      ( ( sdtasasdt0(W0_16654,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != sz00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(W0_16654) )
      | ~ aVector0(W0_16654) ),
    inference(resolution,[status(thm)],[c_114,c_9723]) ).

tff(c_9864,plain,
    ! [W0_16657] :
      ( ( sdtasasdt0(W0_16657,xt) = sz0z00 )
      | ( aDimensionOf0(W0_16657) != sz00 )
      | ~ aVector0(W0_16657) ),
    inference(demodulation,[status(thm),theory(equality)],[c_231,c_231,c_9727]) ).

tff(c_9873,plain,
    ( ( sdtasasdt0(xs,xt) = sz0z00 )
    | ( aDimensionOf0(xs) != sz00 ) ),
    inference(resolution,[status(thm)],[c_116,c_9864]) ).

tff(c_9880,plain,
    sdtasasdt0(xs,xt) = sz0z00,
    inference(demodulation,[status(thm),theory(equality)],[c_195,c_9873]) ).

tff(c_9870,plain,
    ( ( sdtasasdt0(xt,xt) = sz0z00 )
    | ( aDimensionOf0(xt) != sz00 ) ),
    inference(resolution,[status(thm)],[c_114,c_9864]) ).

tff(c_9877,plain,
    sdtasasdt0(xt,xt) = sz0z00,
    inference(demodulation,[status(thm),theory(equality)],[c_231,c_9870]) ).

tff(c_9887,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
    inference(demodulation,[status(thm),theory(equality)],[c_9877,c_122]) ).

tff(c_9915,plain,
    ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
    inference(demodulation,[status(thm),theory(equality)],[c_9880,c_9880,c_9887]) ).

tff(c_9923,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
    inference(demodulation,[status(thm),theory(equality)],[c_324,c_9915]) ).

tff(c_10300,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sz0z00,sz0z00)),
    inference(demodulation,[status(thm),theory(equality)],[c_10287,c_9923]) ).

tff(c_10307,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_410,c_324,c_10300]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 17:59:52 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 10.00/3.32  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.00/3.33  
% 10.00/3.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.12/3.36  
% 10.12/3.36  Inference rules
% 10.12/3.36  ----------------------
% 10.12/3.36  #Ref     : 1
% 10.12/3.36  #Sup     : 2465
% 10.12/3.36  #Fact    : 2
% 10.12/3.36  #Define  : 0
% 10.12/3.36  #Split   : 10
% 10.12/3.36  #Chain   : 0
% 10.12/3.36  #Close   : 0
% 10.12/3.36  
% 10.12/3.36  Ordering : KBO
% 10.12/3.36  
% 10.12/3.36  Simplification rules
% 10.12/3.36  ----------------------
% 10.12/3.36  #Subsume      : 645
% 10.12/3.36  #Demod        : 2134
% 10.12/3.36  #Tautology    : 1002
% 10.12/3.36  #SimpNegUnit  : 63
% 10.12/3.36  #BackRed      : 42
% 10.12/3.36  
% 10.12/3.36  #Partial instantiations: 0
% 10.12/3.36  #Strategies tried      : 1
% 10.12/3.36  
% 10.12/3.36  Timing (in seconds)
% 10.12/3.36  ----------------------
% 10.12/3.36  Preprocessing        : 0.90
% 10.12/3.36  Parsing              : 0.34
% 10.12/3.36  CNF conversion       : 0.26
% 10.12/3.36  Main loop            : 1.38
% 10.12/3.36  Inferencing          : 0.45
% 10.12/3.36  Reduction            : 0.41
% 10.12/3.36  Demodulation         : 0.29
% 10.12/3.36  BG Simplification    : 0.08
% 10.12/3.36  Subsumption          : 0.35
% 10.12/3.37  Abstraction          : 0.06
% 10.12/3.37  MUC search           : 0.00
% 10.12/3.37  Cooper               : 0.00
% 10.12/3.37  Total                : 2.34
% 10.12/3.37  Index Insertion      : 0.00
% 10.12/3.37  Index Deletion       : 0.00
% 10.12/3.37  Index Matching       : 0.00
% 10.12/3.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------